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PROBABILITY
1.
What is the probability of
1.1
getting heads when you throw a coin?
HEADS
TAILS
1
1.2
2
throwing a 1 on a dice?
1
2
3
4
1
6
5
6
2.
If I have 7 balloons at a party, 4 red and 3 yellow, and a blindfolded person has
to pop one, what is the probability that it will be a red one?
1
2
3
4
4
7
5
6
7
3.
If there are 10 balloons at another party,4 red, 3 yellow and 3 green,
what are the chances that a red one will be popped first?
1
2
3
4
5
6
4
10
7
8
9
10
4.
At the heart, a box of smarties breaks open and 12 smarties fall on the floor,
(2 red,3 green, 4 purple, 3 yellow).
Mr Loubser is happy to eat off the floor, so he grabs for a smartie (as do a
couple of other people who are also happy to eat off the floor).
What is the probability that the first one that is picked up is
(i) red?
(ii) purple?
2
4
12
Now for the PROBABILITY TREE:
5.
I have 7 Chinese checkers. 4 red and 3 blue in a box.
a.
If I take one out, what is the probability of it being red?
One red : 4/7
b.
If I take two out, what is the probability of BOTH being red?
Two red : 3/6 x 4/7 = 12/42 = 2/7
c.
If I take two out, what is the probability of one red and one blue?
Can be: first red then blue or first blue then red
First red then blue : 3/6 x 4/7 = 12/42 = 2/7 or first blue then red : 4/6 x 3/7 = 12/42 = 2/7
Probability = 2/7 + 2/7 = 4/7
The complete tree looks like:
R
4/7
R
3/6
RR
3/6 x 4/7
12/42
43
B
3/7
R
B
3/6
RB
3/6 x 4/7
12/42
3
4/6
BR
4/6 x 3/7
12/42
B
2/6
BB
2/6 x 3/7
6/42
6 76
6.
6.1
6.2
There is a lucky draw, based on the colour of the ticket you draw out of a
box (Of course, the box is see through when you draw it. You get R50 if you
draw a yellow ticket and R100 if you draw a green one).
In the box are 6 yellow tickets and 5 green tickets.
If you are allowed to take only 1 ticket, what is the probability of you
drawing a green ticket?
One green : 5/11
If you are allowed to take only two tickets from the box, what is the
probability:
(NB draw a tree diagram)
a.
of drawing 2 green tickets?
Two green : 4/10 x 5/11 = 20/110 = 2/11
b.
of drawing 1 yellow and 1 green ticket?
Can be: first yellow then green or first green then yellow
Yellow then green : 5/10 x 6/11 = 30/110 = 3/11
Probability = 3/11 + 3/11 = 6/11
Or green then yellow : 6/10 x 5/11 = 30/110 = 3/11
Y G
6/11
5/11
Y
5/10
The complete tree looks like:
YY
5/10 x 6/11
30/110
G
Y
5/10
6/10
G
4/10
GG
YG GY
5/10 x 6/11 6/10 x 5/11 4/10 x 5/11
30/110
30/110
20/110
7.
There are 9 buttons in a box. 3 red, 4 white and 2 blue.
Draw a tree diagram to determine the following:
What is the probability of taking a white button?
If you are allowed to take 2 buttons, what is the
probability of their both being white?
If you are allowed to take 2 buttons, what is the
probability of their being 2 different colours?
a.
b.
c.
B
R
3/9
W
2/9
4/9
B
R
2/8
W
4/8
RR
2/8 x 3/9
6/72
RW
4/8 x 3/9
12/72
B
R
2/8
R
RB
2/8 x 3/9
6/72
3/8
WR
3/8 x 4/9
12/72
B
W
3/8
2/8
3/8
WW
3/8 x 4/9
12/72
WB
2/8 x 4/9
8/72
1/8
W
BR
3/8 x 2/9 4/8
6/72
BB
1/8 x 2/9
2/72
BW
4/8 x 2/9
8/72
8.
There are 12 cards in a pack, 4 jacks, 4 queens
and 4 kings.
If you pick a card, what is the probability of
picking a queen?
a.
b.
If you pick a second card, what is the
probability of their both being queens?
(Do a tree diagram)
4/12
K
J
Q
4/12
4/12
K
J
3/11
Q
4/11
JJ
3/11 x 4/12
12/132
J
4/11
K
4/11
Q
3/11
KK
3/11 x 4/12
4/11
4/11
KJ
12/132
4/11 x 4/12 4/11
3/11
16/132
KQ
QQ
4/11 x 4/12
3/11 x 4/12
QJ
QK
16/132
12/132 4/7 x 4/12
4/11 x 4/12
16/132
16/132
JK
4/11 x 4/12
16/132
JQ
4/11 x 4/12
16/132
J
K
Q